In this article, the impact of input pump profile on the gain spectrum as well as the saturation behavior of one-pump fiber optical parametric amplifiers (FOPAs) is investigated. Since in practical circumstances, pump sources used for FOPAs have Lorentz-Gaussian profile instead of Gaussian, a more realistic case is considered for simulating FOPAs in this article. The results of simulations for the Gaussian and the Lorentz-Gaussian profiles show that a higher gain and a faster saturation are obtained for a pump with a Lorentz-Gaussian profile than a Gaussian pump. The results of this article provide a more realistic model for FOPAs.